Minimization of constraint violation probability in model predictive control

Abstract

For Model Predictive Control in safety‐critical systems it is not only important to bound the probability of constraint violation but to reduce this constraint violation probability as much as possible. Therefore, an approach is necessary that minimizes the constraint violation probability while ensuring that the Model Predictive Control optimization problem remains feasible even under changing uncertainty. We propose a novel two‐step Model Predictive Control scheme that yields a solution with minimal constraint violation probability for a norm constraint in an environment with uncertainty. After minimal constraint violation is guaranteed, the solution is then also optimized with respect to other control objectives. Recursive feasibility and convergence of the method are proved. A simulation demonstrates the effectiveness of the proposed method for a collision avoidance example.

Constraint Violation Probability Minimization for Norm-Constrained Linear Model Predictive Control

“…1) Safe Case: Here the set U cvpm is (10) which is the intersection of the admissible input set U N and the set of input sequences that guarantee constraint satisfaction of (5). The set {−Axt} is a singleton that takes into account the current state xt and the set U cvpm is determined with algorithms from [35].…”

“…In the following, we prove recursive feasibility of the safe case, i.e., once the safe case is applicable, XcaseS is invariant under CVPM-MPC. For this purpose, the following assumption is required, which defines the terminal set in (5).…”

Recursively feasible stochastic predictive control using an interpolating initial state constraint -- extended version

“…The issue of recursive feasibility in SMPC formulations was early recognized [15]. Simple modifications include the relaxation of the corresponding chance constraints using penalties [9], [10], minimizing the probability of constraint violation [16], (iteratively) adjusting the probability level in the chance constraints [11], [17], or considering weaker discounted/weighted average probabilistic constraints [12], [13].…”

Safe Stochastic Model Predictive Control

“…However, guaranteeing recursive feasibility in the presence of uncertainty remains a challenge. An MPC approach to minimize constraint violation probability is proposed in [21], but the method is only applicable if norm-based constraints can be employed. In [22], [23] a predictive safety filter is proposed to guarantee safety in probability for reinforcement learning.…”